Renewing the Mainstream Theory of Field and Thermal Electron Emission

Abstract

Mainstream field electron emission (FE) theory—the theory normally used by FE experimentalists—employs a Sommerfeld-type free-electron model to describe FE from a metal emitter with a smooth planar surface of very large extent. This chapter reviews the present state of mainstream FE theory, noting aspects of the history of FE and thermal electron emission theory. It sets out ways of improving the theory’s presentation, with the ultimate aim of making it easier to reliably compare theory and experiment. This includes distinguishing between (a) emission theory and (b) device/system theory (which deals with field emitter behaviour in electrical circuits), and between ideal and non-ideal device behaviours. The main focus is the emission theory. Transmission regimes and emission current density regimes are discussed. With FE, a method of classifying different FE equations is outlined. With theories that assume tunnelling through a Schottky-Nordheim (SN) (“planar-image-rounded”) barrier, a careful distinction is needed between the barrier form correction factor ν (“nu”) and the special mathematical function v (“vee”). This function v is presented as dependent on the Gauss variable x. The pure mathematics of v(x) is summarised, and reasons are given for preferring the use of x over the older convention of using the Nordheim parameter y [=+√x]. It is shown how the mathematics of v(x) is applied to wave-mechanical transmission theory for basic Laurent-form barriers (which include the SN barrier). A brief overview of FE device/system theory defines and discusses different auxiliary parameters currently in use, outlines a preferred method for characterising ideal devices when using FN plots and notes difficulties in characterising non-ideal devices. The chapter concludes by listing some of the future tasks involved in upgrading FE science.